Path planning for a nonholonomic mobile robot is a challenging problem. This paper proposes a novel space adaptive search (SAS) approach that greatly reduces the computation cost of nonholonomic mobile robot path planning. The classic search-based path planning only updates the state on the current location in each step, which is very inefficient, and, therefore, can easily be trapped by local minimum. The SAS updates not only the state of the current location, but also all states in the neighborhood, and the size of the neighborhood is adaptively varied based on the clearance around the current location at each step. Since a great deal of states can be immediately updated, the search can explore the local minimum and get rid of it very fast. As a result, the proposed approach can effectively deal with clustered environments with a large number of local minima. The SAS also utilizes a set of predefined motion primitives, and dynamically scales them into different sizes during the search to create various new primitives with differing sizes and curvatures. This greatly promotes the flexibility of the search of path planning in more complex environments. Unlike the A* family, which uses heuristic to accelerate the search, the experiments shows that the SAS requires much less computation time and memory cost even without heuristic than the weighted A* algorithm, while still preserving the optimality of the produced path. However, the SAS can also be applied together with heuristic or other path planning algorithms.

翻译：非完整移动机器人的路径规划是一个具有挑战性的问题。本文提出了一种新颖的空间自适应搜索方法，该方法极大地降低了非完整移动机器人路径规划的运算成本。经典的基于搜索的路径规划在每一步仅更新当前位置的状态，效率低下，因此容易陷入局部极小值。SAS不仅更新当前位置的状态，还更新邻域内所有状态，并且邻域的大小会根据每一步中当前位置周围的间隙自适应调整。由于大量状态可以立即更新，搜索能够快速探索并摆脱局部极小值。因此，所提方法能有效处理具有大量局部极小值的复杂聚集环境。SAS还利用一组预定义的运动基元，并在搜索过程中动态缩放它们以生成不同尺寸和曲率的新基元。这极大地提升了在更复杂环境中进行路径规划搜索的灵活性。与使用启发式加速搜索的A*系列算法不同，实验表明，即使不使用启发式，SAS所需的计算时间和内存成本也远低于加权A*算法，同时仍能保持生成路径的最优性。然而，SAS也可以与启发式或其他路径规划算法结合使用。